TSTP Solution File: ITP010+2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 17:20:22 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 114 ( 3 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 130 ( 37 ~; 26 |; 47 &)
% ( 3 <=>; 16 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 12 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f311,plain,
$false,
inference(subsumption_resolution,[],[f308,f310]) ).
fof(f310,plain,
p(sF17),
inference(duplicate_literal_removal,[],[f304]) ).
fof(f304,plain,
( p(sF17)
| p(sF17) ),
inference(definition_folding,[],[f236,f303,f302,f301,f303,f302,f301]) ).
fof(f301,plain,
sF15 = c_2Ecardinal_2Ecardleq(sK7,sK8),
introduced(function_definition,[]) ).
fof(f302,plain,
sF16 = ap(sF15,sK9),
introduced(function_definition,[]) ).
fof(f303,plain,
ap(sF16,sK10) = sF17,
introduced(function_definition,[]) ).
fof(f236,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( ne(sK7)
& mem(sK9,arr(sK7,bool))
& ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) )
& mem(sK10,arr(sK8,bool))
& ne(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f149,f153,f152,f151,f150]) ).
fof(f150,plain,
( ? [X0] :
( ne(X0)
& ? [X1] :
( ? [X2] :
( mem(X2,arr(X0,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) ) )
& ne(X1) ) )
=> ( ne(sK7)
& ? [X1] :
( ? [X2] :
( mem(X2,arr(sK7,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) ) )
& ne(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f151,plain,
( ? [X1] :
( ? [X2] :
( mem(X2,arr(sK7,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) ) )
& ne(X1) )
=> ( ? [X2] :
( mem(X2,arr(sK7,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),X2),X3)) )
& mem(X3,arr(sK8,bool)) ) )
& ne(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
( ? [X2] :
( mem(X2,arr(sK7,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),X2),X3)) )
& mem(X3,arr(sK8,bool)) ) )
=> ( mem(sK9,arr(sK7,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),X3)) )
& mem(X3,arr(sK8,bool)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),X3)) )
& mem(X3,arr(sK8,bool)) )
=> ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) )
& mem(sK10,arr(sK8,bool)) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
? [X0] :
( ne(X0)
& ? [X1] :
( ? [X2] :
( mem(X2,arr(X0,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) ) )
& ne(X1) ) ),
inference(flattening,[],[f148]) ).
fof(f148,plain,
? [X0] :
( ne(X0)
& ? [X1] :
( ? [X2] :
( mem(X2,arr(X0,bool))
& ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) ) )
& ne(X1) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f91,plain,
? [X0] :
( ne(X0)
& ? [X1] :
( ? [X2] :
( mem(X2,arr(X0,bool))
& ? [X3] :
( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<~> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) ) )
& ne(X1) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,plain,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) ) ) ) ) ),
inference(rectify,[],[f42]) ).
fof(f42,negated_conjecture,
~ ! [X8] :
( ne(X8)
=> ! [X9] :
( ne(X9)
=> ! [X13] :
( mem(X13,arr(X8,bool))
=> ! [X14] :
( mem(X14,arr(X9,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X13),X14))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X13),X14)) ) ) ) ) ),
inference(negated_conjecture,[],[f41]) ).
fof(f41,conjecture,
! [X8] :
( ne(X8)
=> ! [X9] :
( ne(X9)
=> ! [X13] :
( mem(X13,arr(X8,bool))
=> ! [X14] :
( mem(X14,arr(X9,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X13),X14))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X8,X9),X13),X14)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f308,plain,
~ p(sF17),
inference(duplicate_literal_removal,[],[f305]) ).
fof(f305,plain,
( ~ p(sF17)
| ~ p(sF17) ),
inference(definition_folding,[],[f235,f303,f302,f301,f303,f302,f301]) ).
fof(f235,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK7,sK8),sK9),sK10)) ),
inference(cnf_transformation,[],[f154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 23:31:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.51 % (5780)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.51 % (5792)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.52 % (5793)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52 % (5802)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.52 % (5790)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52 % (5792)First to succeed.
% 0.19/0.52 % (5794)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.52 % (5800)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.52 TRYING [1]
% 0.19/0.53 % (5785)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.53 % (5784)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53 % (5801)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.53 % (5804)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.53 % (5808)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.53 % (5781)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53 % (5782)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.53 % (5806)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.53 % (5786)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53 % (5789)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53 % (5792)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (5792)------------------------------
% 0.19/0.53 % (5792)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (5792)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (5792)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (5792)Memory used [KB]: 5628
% 0.19/0.53 % (5792)Time elapsed: 0.011 s
% 0.19/0.53 % (5792)Instructions burned: 8 (million)
% 0.19/0.53 % (5792)------------------------------
% 0.19/0.53 % (5792)------------------------------
% 0.19/0.53 % (5779)Success in time 0.186 s
%------------------------------------------------------------------------------